# How important is parameter uncertainty around the UK EQ-5D-3L value set when estimating treatment effects?

##### Gray A., Rivero Arias O., Leal J., Dakin HA., Ramos Goñi JM.

Aims: The uncertainty around the EQ-5D-3L value set is commonly ignored in economic evaluation. This study evaluates the impact of including parameter uncertainty around the original UK EQ-5D-3L value set (or “tariff”) within standard errors as well as sampling uncertainty around the trial population. Methods: First, we re-estimated the N3 model of the EQ-5D-3L value set with original data from the Measurement and Valuation of Health (MVH) study to replicate the published coefficients. Second, we estimated standard errors around the predicted utility of each EQ-5D-3L health state to evaluate the impact of parameter uncertainty on these estimated utilities. Third, we used a two-stage bootstrap approach to combine the resulting MVH parameter uncertainty with trial sampling uncertainty for a large randomised trial population. In the first step, we generated 1,000 sets of coefficients for the UK EQ-5D-3L tariff using bootstrap resampling from the original MVH sample. In the second step, we used bootstrap resampling from the clinical trial data 10,000 times for each of the 1,000 sets of EQ-5D tariff coefficients. The standard error including MVH parameter uncertainty was then estimated as the standard deviation across the resulting vector of results from the 10 million bootstrap replicates. This figure was compared against a one-stage bootstrap from the clinical trial sample to assess the impact of including parameter uncertainty. Data: The EQ-5D N3 model was estimated using the original MVH data. The randomised control trial used as a case study was the International Subarachnoid Aneurysm Trial (ISAT), a large clinical trial comparing endovascular coiling and neurosurgery for the treatment of ruptured aneurysms. EQ-5D-3L data to calculate mean utilities at 2 and 12 months’ follow-up and the quality-adjusted life years (QALYs) accrued over the trial period were available for 1633 patients. Findings: Including MVH parameter uncertainty around the original EQ-5D N3 model increased the standard errors around mean between-group differences in utility only very slightly from 0.01542 (ignoring parameter uncertainty) to 0.01550 at 2 months follow-up, from 0.01490 to 0.01493 at 12 months follow-up and from 0.01149 to 0.01155 for QALYs. Sensitivity analysis suggests parameter uncertainty has a larger impact when the N3 model is re-estimated using much smaller valuation samples: estimates based on a 1% sub-sample of MVH respondents increases the variance by 5.60% at 2 months follow-up, 4.87% at 12 months follow-up and 4.59% for QALYs. The standard errors around with the original time trade-off valuations in the MVH study suggests a substantial amount of between respondent variation affecting most health states, which the original N3 model did not fully account for. Therefore, the standard errors around N3 model predictions are likely to be biased, and do not reflect the true uncertainty around the valuations. Conclusions/implications: Our results suggest that parameter uncertainty around the EQ-5D value set has little impact on the estimated confidence intervals around utility differences in this example. This result is driven by the precision of the original estimated coefficients, given the large dataset used in the original MVH study. However, parameter uncertainty may have more influence on value sets estimated using different estimation methods or smaller valuation samples. Our results suggest that other types of uncertainty around health state valuations, such as model uncertainty, may have more important implications than parameter uncertainty: further research is required to clarify this.